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Article: Amplitude incremental variational principle for nonlinear vibration of elastic systems

TitleAmplitude incremental variational principle for nonlinear vibration of elastic systems
Authors
Issue Date1981
PublisherASME International. The Journal's web site is located at http://asmedl.aip.org/AppliedMechanics
Citation
Journal of Applied Mechanics, Transactions Asme, 1981, v. 48 n. 4, p. 959-964 How to Cite?
AbstractThe incremental method has been widely used in various types of nonlinear analysis, however, so far it has received little attention in the analysis of periodic nonlinear vibrations. In this paper, an amplitude incremental variational principle for nonlinear vibrations of elastic systems is derived. Based on this principle various approximate procedures can be adapted to the incremental formulation. The linear solution for the system is used as the starting point of the solution procedure and the amplitude is then increased incrementally. Within each incremental step, only a set of linear equations has to be solved to obtain the data for the next stage. To show the effectiveness of the present method, some typical examples of nonlinear free vibrations of plates and shallow shells are computed. Comparison with analytical results calculated by using elliptic integral confirms that excellent accuracy can be achieved. The technique is applicable to highly nonlinear problems as well as problems with only weak nonlinearity.
Persistent Identifierhttp://hdl.handle.net/10722/149840
ISSN
2015 Impact Factor: 1.394
2015 SCImago Journal Rankings: 0.630

 

DC FieldValueLanguage
dc.contributor.authorLau, SLen_US
dc.contributor.authorCheung, YKen_US
dc.date.accessioned2012-06-26T06:00:04Z-
dc.date.available2012-06-26T06:00:04Z-
dc.date.issued1981en_US
dc.identifier.citationJournal of Applied Mechanics, Transactions Asme, 1981, v. 48 n. 4, p. 959-964en_US
dc.identifier.issn0021-8936en_US
dc.identifier.urihttp://hdl.handle.net/10722/149840-
dc.description.abstractThe incremental method has been widely used in various types of nonlinear analysis, however, so far it has received little attention in the analysis of periodic nonlinear vibrations. In this paper, an amplitude incremental variational principle for nonlinear vibrations of elastic systems is derived. Based on this principle various approximate procedures can be adapted to the incremental formulation. The linear solution for the system is used as the starting point of the solution procedure and the amplitude is then increased incrementally. Within each incremental step, only a set of linear equations has to be solved to obtain the data for the next stage. To show the effectiveness of the present method, some typical examples of nonlinear free vibrations of plates and shallow shells are computed. Comparison with analytical results calculated by using elliptic integral confirms that excellent accuracy can be achieved. The technique is applicable to highly nonlinear problems as well as problems with only weak nonlinearity.en_US
dc.languageengen_US
dc.publisherASME International. The Journal's web site is located at http://asmedl.aip.org/AppliedMechanicsen_US
dc.relation.ispartofJournal of Applied Mechanics, Transactions ASMEen_US
dc.titleAmplitude incremental variational principle for nonlinear vibration of elastic systemsen_US
dc.typeArticleen_US
dc.identifier.emailCheung, YK:hreccyk@hkucc.hku.hken_US
dc.identifier.authorityCheung, YK=rp00104en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.scopuseid_2-s2.0-0019668332en_US
dc.identifier.volume48en_US
dc.identifier.issue4en_US
dc.identifier.spage959en_US
dc.identifier.epage964en_US
dc.publisher.placeUnited Statesen_US
dc.identifier.scopusauthoridLau, SL=7401596228en_US
dc.identifier.scopusauthoridCheung, YK=7202111065en_US

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